If a constant torque acts on a body, the body?

Options

A. will acquire a linear acceleration according to Newton's second law of motion
B. will acquire angular momentum
C. will rotate with a constant angular velocity
D. the body will move with a constant velocity or remain motion less in accordance with Newton's first law of motion.

Answer

To solve the question "If a constant torque acts on a body, the body?" we will analyze the implications of a constant torque on the motion of the body step by step.

### Step-by-Step Solution:

1. **Understanding Torque**:
Torque (τ) is defined as the product of the force (F) applied and the distance (r) from the pivot point where the force is applied. Mathematically, it is given by:
\[ τ = r \times F \]
If a constant torque is applied, it means that the torque value does not change over time.

**Hint**: Remember that torque is related to the rotational effect of a force applied at a distance from the axis of rotation.

2. **Effect of Constant Torque**:
According to the rotational analog of Newton's second law, the net torque acting on a body is equal to the moment of inertia (I) of the body multiplied by its angular acceleration (α):
\[ τ = I \cdot α \]
If the torque is constant, then the angular acceleration will also be constant.

**Hint**: Think about how constant torque leads to constant angular acceleration, which affects the angular velocity of the body.

3. **Angular Velocity and Angular Acceleration**:
The relationship between angular velocity (ω), angular acceleration (α), and time (t) can be expressed as:
\[ ω = ω_0 + α \cdot t \]
where \(ω_0\) is the initial angular velocity. Since α is constant, the angular velocity will change over time as long as torque is applied.

**Hint**: Consider how the body’s angular velocity changes over time due to the constant angular acceleration.

4. **Angular Momentum**:
Angular momentum (L) is given by:
\[ L = I \cdot ω \]
Since the body is experiencing a constant torque, it will also experience a change in angular momentum over time. The angular momentum will increase as the body rotates.

**Hint**: Remember that angular momentum is directly related to both the moment of inertia and the angular velocity.

5. **Conclusion**:
Given that a constant torque results in a constant angular acceleration, which in turn leads to a change in angular velocity and an increase in angular momentum, the most appropriate answer to the question is:
- The body will acquire angular momentum.

### Final Answer:
**The body will acquire angular momentum.**